Method for correcting DC offsets in a receiver

ABSTRACT

A method for reducing DC offset from a receiver signal. The method includes jointly (i.e., simultaneously) estimating such DC offset and channel impulse response, and reducing the DC offset in accordance with the estimated DC offset and the estimate of the channel impulse response.

BACKGROUND OF THE INVENTION

This Application is a continuation of Ser. No. 09/310,612 filed May 12,1999, now U.S. Pat. No. 6,504,884.

This invention relates generally to radio frequency receivers and moremethods for reducing DC offsets in such receivers.

As is known in the art, received radio frequency signals are convertedto baseband using various receivers. With a homodyne receiver, thereceived radio frequency signal is mixed with the local oscillator whosefrequency is equal to carrier frequency of the received radio frequencysignal to translate the carrier frequency to DC and thereby provide“direct conversion” of the modulation on the received radio frequencysignal to a modulation at DC. Hence, a homodyne receiver is sometimesreferred to as a direct conversion receiver.

While such direct conversion receivers offer the advantage of reducedcost, DC offset associated with such receivers presents a major problemfor receiver performance. More particularly, DC offset is produced fromthe homodyning. The level of the DC offset may be significantly largerthan the desired signal, i.e., modulation, to be demodulated. Thus, DCoffset compensation techniques are typically required. Toinsure-flexibility for different operating conditions, DC offsetcompensation can be part of the digital baseband portion of thereceiver, preferably a part of the digital signal processing (DSP)firmware. One application of direct conversion receivers is in mobile orcellular communication systems. In such systems, the radio channelsreceived signals also suffer from intersymbol interference (ISI) causedby multipath radio propagation and transmitter and/or receiverfiltering.

More particularly, various DC offset compensation techniques, for bothanalog and digital domain, have been suggested. With regard to theGlobal System for Mobile Communications (GSM) environment, thesesuggested techniques are largely dependent on the sources of DC offsetsince they result in different levels of DC offset compared to thedesired signal level. As discussed in an article entitled “Designconsiderations for direct-conversion receivers,” by B. Rezavi, publishedin IEEE Transactions on circuits and systems—II: analog and digitalsignal processing, June 97, pp 428-435, two major mechanisms causing DCoffset in direct conversion receivers are: Local Oscillator (LO)isolation to the receiver's Low Noise Amplifier (LNA) and mixer inputs;and interference leakage to the LO (i.e., self mixing). The level of DCoffset in this case is much larger than the level of the desired signal.

Various techniques have been suggested to remove DC offset generated bythese two major mechanism. Included in these techniques are: ACcoupling; Offset cancellation using capacitor; Sample mean (average)estimation; Adaptive DC offset compensation for burst mode operation;and Re-integration.

AC coupling, requires high-pass filter with corner frequency 0.1% of thedata rate, which is less that 270 Hz for GSM. Problems associated withthis approach are elimination of signal content around DC, group delaycharacteristic of the filter and settling time in Time Division MultipleAccess (TDMA) environment.

With offset cancellation using a capacitor for TDMA systems, the offsetin the receive path can be stored on a capacitor during the idle modeand subtracted from the signal during actual reception in the burst. Themajor issues with this technique are kT/C noise and problems wheninterferer is stored along with other offsets.

With the sample mean (average) estimation based technique, suchtechnique includes averaging over sufficiently long period andsubtraction, as described by A. Bateman and D. Haines, in “Directconversion transceiver design for compact low-cost portable mobile radioterminals,” in Proc. VTC'89, pp 57-62. In TDMA systems, averaging isusually performed over the burst duration. The issues associated withthis approach are: it does not address DC offset changes within burst;and it may introduce some bias since burst does not have zero DCcomponent due to different number of zeros and ones in the data stream.Besides its simplicity this method has some desirable statisticalproperties. Sample mean estimate is optimal DC offset estimate inzero-mean noise with Gaussian probability density function in minimummean-squared error sense (also minimum variance unbiased estimate) andmaximum likelihood sense. Even when the probability density function(pdf) of the noise is not known, the signal average is the best linearunbiased estimate, see Fundamentals of statistical signal processing:estimation theory, Prentice Hall, 1993 by S. Kay.

Adaptive DC offset compensation for burst mode operation is presented ina paper entitled “Adaptive DC offset compensation algorithm for burstmode operated direct conversion receivers,” by S. Sampei and K. Feher,Proc. VTC'92, pp 93-96. This approach utilizes the known bits from thepreamble to acquire DC offset, typically 3-5 bits. Simulations haveshown that the technique is efficient in the cases where the DC offsetratio (amplitude ratio of DC offset to the maximum amplitude of thetransmitted symbol) is less than 40%. Degradation of the performance isup to 1.5 dB. A similar approach has been presented by J. Bergmans,Digital baseband transmission and recording, Kluwer Academic Publishers,Section 8.8.2. in a more general communication scenario of continuousreception. In essence it is a form of dynamic loop tracking DC offset.

Digital compensation based on Least Mean Square (LMS) adaptive algorithmhas been presented in by J. Cavers and M. Liao, in “Adaptivecompensation for imbalance and offset losses in direct conversionreceivers,” IEEE Transactions on Vehicular Technology, November 93, pp581-588. Such paper describes models and theoretical development ofreceiver and transmitter compensation (modulator and demodulator). Theleast mean square (LMS) algorithm has been applied to set the parametersof the compensating circuit (compensates for In-Phase (I) and Quadrature(Q) gain and phase imbalance and DC offset). Effectively the system hasthree adaptive coefficients. A drawback of the algorithm is the longconvergence time and sensitivity to the selection of LMS step-sizeparameters.

The re-integration approach is presented in a paper by B. Lindquist, M.Isberg and P.Dent, entitled “A new approach to eliminate the DC offsetin a TDMA direct conversion receiver,” In Proc. VTC'93, pp 754-757 [7].The idea is to differentiate signal, digitize it and then re-integrate,thus eliminating DC component. It is based on adaptive delta modulationand since there is no time constant it targets TDMA direct conversionreceivers. Simulation results presented in the paper indicate signal tonoise ratio (SNR) degradation of 1 dB in static channel for the BitError Rate (BER) range 1% to 0.1%.

In a GSM system, the whole burst is stored and the all-digitaltechniques described above may be adapted to extract DC offset. Thus,referring to FIG. 1, the data receiver stores the burst of data, r(k),where k=1 . . . N and N is the number of samples in the burst. Eachburst includes a mid-amble having a known sequence of bits disposedbetween data, (i.e., information bits) as shown. Such known sequence ofbits is used to aid in equalization and more particularly for enablingcomputation of the channel impulse response (CIR). As shown in FIG. 1,an estimate of the DC offset, Â, is calculated. The estimated DC offset,Â, where k=1 . . . N, is subtracted from the received burst. The result,r(k)−Â, where k=1 . . . N, is processed to find an estimate of thechannel impulse response (CIR), ĥ. The estimate of the channel impulseresponse (CIR), ĥ, can be obtained by cross-correlating [r(k)−{rightarrow over (A)}] with the known mid-amble bit sequence.

The complexity of the DC offset cancellation in GSM system is related toother signal processing functions performed in baseband(synchronization, equalization). Residual DC offset may affect theperformance of data receiver.

SUMMARY OF THE INVENTION

In accordance with the present invention, a method is provided forreducing DC offset from a received signal. The method includes jointlyestimating such DC offset and a channel impulse response, ĥ, andreducing the DC offset in accordance with the estimated DC offset andthe estimated channel impulse response, ĥ.

In accordance with another feature of the invention, a communicationsystem is provided wherein information is transmitted through a channelhaving a discrete channel impulse response h(k), where k is a timeindex, to produce at an output of the channel, a signal, r(k), where:${r(k)} = {A + {\sum\limits_{n}{{b(n)}{h\left( {k - n} \right)}}} + {N(k)}}$

where:

A is DC offset; $\sum\limits_{n}{{b(n)}{h\left( {k - n} \right)}}$

is a modulated signal transmitted over the channel 42;

b(n) are transmitted data symbols; and

N(k) is additive noise.

The system includes a receiver for receiving the transmittedinformation. The receiver has a processor programmed to solve thefollowing equations simultaneously:$\frac{\partial{f\left( {e(k)} \right)}}{\partial\hat{A}} = 0$$\frac{\partial{f\left( {e(k)} \right)}}{\partial\hat{h}} = 0$

where:

f(e(k)) is a function, usually quadratic, of the estimation error, e(k),where

e(k) is the difference between the received signal and an estimate ofthe received signal; i.e.,${e(k)} = {{r(k)} - \hat{A} - {\sum\limits_{n}\left\lbrack {{b(n)}\hat{h}\left( {k - n} \right)} \right\rbrack}}$

In accordance with another feature of the invention, a communicationsystem is provided wherein information is transmitted through a channelas a series of bursts, each burst having a predetermined series of bitsand a series of information bits. The system includes a receiver forreceiving the transmitted information. The receiver has a processorprogrammed to simultaneously solve the following equations from: (a) thepredetermined series of bits; (b) a tentative decision of theinformation bits; or, a combination of the predetermined series of bitsand the tentative decision of the information bits:$\frac{\partial{f\left( {e(k)} \right)}}{\partial\hat{A}} = 0$$\frac{\partial{f\left( {e(k)} \right)}}{\partial\hat{h}} = 0$

where:

f(e(k)) is a function, usually quadratic, of the estimation error, e(k),where

e(k) is the difference between the received signal and an estimate ofthe received signal; i.e.,$\left. {{e(k)} = {{r(k)} - \hat{A} - {\underset{n}{\sum\lbrack}{b(n)}{\hat{h}\left( {k - n} \right)}}}} \right\rbrack$

BRIEF DESCRIPTION OF THE DRAWING

These and other features of the invention will become more readilyapparent from the following detailed description when taken togetherwith the following drawings, in which:

FIG. 1 is a block diagram of a data receiver in accordance with thePRIOR ART;

FIG. 2 is a block diagram of a radio communication system according tothe invention;

FIG. 3 is a block diagram of a data receiver used in the radiocommunication system of FIG. 2 according to the invention;

FIG. 4 is a flowchart showing the process used to jointly estimate DCoffset and the channel impulse response for the system of FIG. 2according to the invention;

FIG. 5 is a flowchart showing the process used to jointly estimate DCoffset and the channel impulse response for the system of FIG. 2 basedon Least Mean Square error, sample by sample over a burst durationaccording to one embodiment of the invention;

FIG. 6 is a flowchart showing the process used to jointly estimate DCoffset and the channel impulse response for the system of FIG. 2 basedon Least Square Error, by processing over an entire burst in a specifiednumber of iterations, according to another embodiment of the invention;

FIG. 7 shows the probability density function (pdf) estimate of the DCoffset estimation error for high signal-to-noise ratio (SNR), i.e., withno noise, according to the PRIOR ART (i.e., “sample mean”) and accordingto the invention (i.e., “joint estimate”) performed over the entireburst;

FIG. 8 shows the probability density function (pdf) estimate of the DCoffset estimation error for a SNR=8 db, for both the PRIOR ART methodand in accordance with the invention over the entire burst;

FIG. 9 shows the probability density function (pdf) estimate of the DCoffset estimation error for a SNR=8 db, for both the PRIOR ART methodand in accordance with the invention over the mid-amble portion of theburst; and

FIG. 10 shows bit error rate (BER) as a function of Energy per bit/Noisedensity, (Eb/No), for no DC offset compensation, a compensationaccording to the PRIOR ART method, and in accordance with the inventionover both the whole burst N (JE-N) and over the mid-amble portion of theburst M (JE-M).

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to FIG. 2, a block diagram of a communication system 10,here a TDMA communication system is shown to include a transmitter, hererepresented by a transmitter 12 for producing a radio frequency carriermodulated by bursts of data bits. Each burst includes a known sequenceof bits and a series of unknown, here information, bits. Such knownsequence of bits is used to aid in equalization and more particularlyfor enabling computation of the channel impulse response (CIR). Forexample, with a GSM, each burst includes a mid-amble having a knownsequence of bits interposed between a pair of series of information,bits. Here, the mid-amble is used in a manner to be described to reduceDC offset from a receiver signal by jointly estimating such DC offsetand the channel impulse response, and reducing the DC offset inaccordance with the estimated DC offset and the estimated channelimpulse response.

More particularly, the information, after passing through a data blockgenerator 14, interleaver 18, burst formatter 20, modulator and analogto digital converter (ADC) 22 is transmitted by a transmitter 24 throughspace (i.e., a radio propagation channel 26) to a receiver 28. Moreparticularly, the receiver 28 is a direct conversion receiver having ahomodyning receive section 30, an ADC 32, a data receiver 34 (to bedescribed in detail in FIG. 3), a burst demodulator 36, a de-interleaver38, and a decoder 40. It is noted that a channel 42 is thereby providedbetween the output of the burst formatter 20 and the output of ADC 32.Such channel 42 may be characterized by a discrete impulse responseh(k), where k is a time index.

The receive section 30 includes an antenna 43 for receiving thetransmitted radio frequency signal having a carrier frequency f_(o). Theradio frequency signal carrier is modulated with desired data at thetransmitter, in any conventional manner. Here, the receiver is used in aTime Domain Multiple Access (TDMA) system. The antenna 43 is fed to amixer 44, as shown. Also fed to the mixer 44 is a local oscillatorsignal produced by local oscillator (LO) generator 46. Here, thefrequency of the signal produced by the local oscillator is also f_(o).The output of mixer 44 is passed through low pass filter 48 to removehigher-order harmonics from the mixing process. The resulting basebandsignal, here a train of bursts, produced at the output of the low passfilter is fed to the analog to digital converter (ADC) 32 where themodulation is converted to corresponding digital data. The data isprocessed in the data receiver 34 which includes a Digital SignalProcessor (DSP), as indicated.

Referring to FIG. 3, the data receiver 34 is shown to include a burststorage, or memory, 50, used by a DSP 52 to remove the DC offset fromthe burst, and to provide equalization which is assisted by a jointestimate of both the DC offset, Â, and the channel impulse response, ĥ.In order to understand the process used to remove the DC offset, A, letit first be assumed that dynamic range of the converter is large enoughto accommodate both DC offset and the desired signal (i.e., themodulation at baseband), and that the sampled version of the complexbaseband signal at the output of the analog to digital converter (ADC)34 can be represented as:${r(k)} = {A + {\sum\limits_{n}{{b(n)}{h\left( {k - n} \right)}}} + {N(k)}}$

where:

A is the DC offset;$\sum\limits_{n}{{b(n)}{h\left( {k - n} \right)}}$

is the modulated signal received by the ADC;

k is a time index;

b(n) are data symbols;

h(k) is the impulse response of channel 42 (i.e., from transmitterbaseband to receiver baseband) and includes the modulator 22, thetransmitter 24, the radio propagation channel 26, the R. F. receiver 30and ADC 32; and

N(k) is additive noise.

This formulation is quite general since it captures complex (i.e.,In-Phase (I) and Quadrature (Q)) signal.

The received signal includes three terms: (1) the DC offset; (2) thesignal passed through the channel 42, i.e., the modulated signal; and(3) thermal noise. Intuitively, if we are able to remove effect ofmodulated signal, we will reduce overall noise in the process of DCoffset estimation.

The problem can be formulated as joint estimation problem of unknown DCoffset and channel 42 coefficients which represent the estimate of thechannel impulse response. Such channel 42 coefficients are required forthe data receiver 34 equalizer 53 (FIG. 3) provided by the DSP 52. Thatis, we want to minimize a function of the error e(k) with respect to theestimated DC offset, Â, simultaneously with the minimizing the errore(k) with respect to the channel impulse response, ĥ, where e(k) is afunction of the actual received modulated signal, r(k), and theestimated modulated signal, {circumflex over (r)}, where k is the timeindex. That is, the DC offset and channel impulse response are jointlyestimate. In order to perform this joint minimization of f(e), weresolve the following two equations simultaneously:$\frac{\partial{f\left( {e(k)} \right)}}{\partial\hat{A}} = 0$$\frac{\partial{f\left( {e(k)} \right)}}{\partial\hat{h}} = 0$

$\left. {{e(k)} = {{r(k)} - \hat{A} - {\underset{n}{\sum\lbrack}{b(n)}{\hat{h}\left( {k - n} \right)}}}} \right\rbrack$

In a GSM system, for example, we constrain the estimate of ĥ to achannel length to 5 coefficients based on physical channel profiles. Inthat case, the received signal can be expressed in the vector form,where the symbols: *; T; and, H are for conjugate, transpose andHermitian (conjugate and transpose) respectively:

r(k)=A+{right arrow over (h)} ^(H) {right arrow over (b)}(k)+N(k)

where:

→ represents a vector; and

{right arrow over (h)}=[h ₀ . . . h _(L)]^(T)

is the channel vector of length (L+1) assumed to be fixed within aburst, and the corresponding data vector is

{right arrow over (b)}(k)=[b(k) . . . b(k−L)]^(T)

Here, f(e(k)) is the Minimum Mean Square Error function. Theoptimization criterion is the Minimum Mean-Squared Error (MMSE), wheresymbol E{ } denotes statistical average.${\min\limits_{A,\overset{->}{h}}{E\left\{ {{e(k)}}^{2} \right\}}},{{e(k)} = {{r(k)} - A - {\overset{\quad {->H}}{h}{\overset{->}{b}(k)}} - {N(k)}}}$

Differentiating with respect to the DC offset value and the estimatedchannel impulse response and equating the obtained gradients to zero thecoupled system of equations is obtained. That is:$\frac{{\partial E}{{e(k)}}^{2}}{\partial\overset{\rightarrow}{h}} = 0$$\frac{{\partial E}{{e(k)}}^{2}}{\partial A} = 0$

The simultaneous solution results in:

A _(o) =E{r(k)−{right arrow over (h)} _(o) ^(H) {right arrow over(b)}(k)}

{right arrow over (h)} _(o) =E{{right arrow over (b)}(k){right arrowover (b)} ^(H)(k)}⁻¹ E{{right arrow over (b)}(k)[r(k)−A _(o)]*}

These equations provide optimal solution in MMSE sense (It is importantto note that using maximum likelihood criterion we would obtain the samesolution since the additive noise is assumed to have Gaussiandistribution).

The following should be noted: Provided that we have a statisticalaverage (which is not the case in practice and which will be addressedlater), the solution is intuitive: DC offset is calculated by averagingover the received samples once the channel impact is removed and theestimated channel impulse response (i.e, coefficients) are obtainedafter removing DC offset from received samples. Because the equationsare cross-coupled, we have to start the iterative process, i.e. estimateone of the parameters first and then proceed with the computation havingin mind that DC offset can be much larger than the desired signal. Aninitial estimate of the DC offset can be average over received samplesneglecting the channel impact. This is also intuitive: The statisticalaverage of the modulated signal, here, for example, a Gaussian MinimumShift Keying (GMSK) received signal, is zero. In addition we canapproximate desired signal passed through fading channel as Gaussiandistributed (channel coefficients of fading channel are complex Gaussianin European Telecommunication Standard Institute (ETSI) models). In thatcase, the optimal DC offset estimate in the zero-mean noise withGaussian probability density function (pdf) is given by received signalaverage, which is optimal in MMSE and in the maximum likelihood sense.Even when pdf of noise is not known, the signal average is best linearunbiased estimate. The timing estimate within the burst has to becalculated. Because it is extracted from mid-amble portion, it should beperformed after DC offset removal.

Since the statistical average is not available in practical system dueto finite length of received samples (GSM burst), there are severalapproaches to implement the optimal solution. All of them are based oncertain approximation of the statistical averaging operator.

General Solution

The process for reducing DC offset from a direct conversion receiversignal is performed by jointly estimating such DC offset and channelimpulse response (i.e. coefficients representing channel 42 (FIG. 2))and reducing the DC offset in accordance with the estimated DC offsetand estimated channel impulse response. More particularly, referring toFIG. 4, the DSP 52 is programmed by a memory in the DSP 52 in accordancewith the flowchart shown in FIG. 4, to perform the following method onthe received signal, r(k). In step 100, the received burst samples, r(k)are stored in a memory 55 of the DSP 52. Next, in step 102, a joint,i.e., simultaneous, Minimum Mean Square Error optimization with respectto the DC offset, A, and channel impulse response (i.e., coefficientvector, {right arrow over (h)}(k)), is performed resulting in a coupledsystem of equations that are solved simultaneously:

A _(o) =E{r(k)−{right arrow over (h)} _(o) ^(H) {right arrow over(b)}(k)}

{right arrow over (h)} _(o) =E{{right arrow over (b)}(k){right arrowover (b)} ^(H)(k)}⁻¹ E{{right arrow over (b)}(k)[r(k)−A _(o)]*}

Next, in step 104, the computed DC offset, A_(o), and the computedchannel impulse response, {right arrow over (h)}_(o), (i.e., coefficientvector ({right arrow over (h)}_(o))) are forwarded to the data receiver34, FIG. 3.

Thus, referring to FIG. 3, the stored r(k) has the DC offset thereof, A,removed by subtracting the computed DC offset, A₀, from the stored r(k)in subtractor 51 to produce the signal r(k)−A₀. The signal, r(k)−A₀, isfed to equalizer 53 along with the computed channel impulse response,{right arrow over (h)}_(o), to aid in equalization and ISI reduction.

Adaptive Solution Based on LMS

Having the gradient of the solution, we can replace the statisticalaverage by single point approximation. In that case, an adaptivealgorithm for joint estimation can be summarized as:

1. Calculate initial values:${A(0)} = {\frac{1}{N}{\sum\limits_{k = 1}^{N}{r(k)}}}$

and

 h(0)=0

N being the number of samples required for averaging (up to burstlength).

2. Subtract A(0) from received samples and extract timing

3. For n=0, 1, 2 . . .

e(n)=r(n)−{right arrow over (h)} ^(H)(n){right arrow over (b)}(n)−A(n)

A(n+1)=A(n)+μe(n)

{right arrow over (h)}(n+1)={right arrow over (h)}(n)+μ{right arrow over(b)}(n)e*(n)

4. Subtract the DC offset value from received samples for furtherprocessing, where μ is the Least Mean Square (LMS) step-size parameterdetermined for each specific system being designed though simulation ofthe system. From the computational point of view, this solution is verysimple. It requires only one inner product in error calculation. Apotential problem for the LMS solution is the long convergence time,which can be much higher than mid-amble length. Therefore, we have torely on tentative decisions feedback from receiver equalizer 53 (FIG.3). On the other hand, the adaptive solution could track slow changes inthe DC offset and the channel response within the burst.

Thus, referring to FIG. 5, the DSP 52 is programmed by a memory storedin the DSP 52 in accordance with the flowchart shown in FIG. 5, toperform the following method on the received signal, r(k):

In step 200, the received burst samples, r(n), where n goes from 1 to N,are stored in a memory provided in the DSP 52. In the next step, 202, aninitial DC offset, A(0), is calculated from the received samples as theaverage value over the burst. In the next step 204, the initial DCoffset, A(0), is subtracted from the received burst, r(n), where n=1 . .. N, (i.e, r(n)−A(0). In the next step 206, an error function,e(n)=r(n)−{right arrow over (h)}^(H)(n){right arrow over (b)}(n)−A(n) iscalculated. In the next step 208, an update of the DC offset value,A(n+1)=A(n)+μe(n) is performed. In the next step 210, an update thechannel impulse response (i.e., coefficient vector value) {right arrowover (h)}(n+1)={right arrow over (h)}(n)+μ{right arrow over (b)}(n)e*(n)is performed. In the next step 212, the computed DC offset A(n+1) andchannel impulse response (i.e., coefficient vector) {right arrow over(h)}(n+1) are forwarded to the data receiver 34 at each sample instantn. The process returns to step 206 until the end of the burst, step 214.When the burst is ended, the DSP 52 proceeds to data receiver 34 anddecoding (i.e., decoder 40, FIG. 2), step 216.

Another possibility for the adaptive solution is to employ RecursiveLeast-Squares (RLS), however it is more computationally intensive.

Least-Squares Solution

The solution using the deterministic criterion of least-squares has thesame form as the optimal MMSE solution except that the statisticalaverage is replaced by a time average. Again, it is important to notethat the DSP 52 is programmed to simultaneously solve the equations:$\frac{\partial{f\left( {e(k)} \right)}}{\partial\hat{A}} = 0$$\frac{\partial{f\left( {e(k)} \right)}}{\partial\hat{h}} = 0$

described above from: (a) the predetermined series of bits; (b) atentative decision of the information bits; or, a combination of thepredetermined series of bits and the tentative decision of theinformation bits.

The Least-squares solution can be summarized as:

1. Calculate initial value${A(0)} = {\frac{1}{N}{\sum\limits_{k = 1}^{N}{r(k)}}}$

N being the number of samples required for averaging (up to burstlength, N, to be determined by simulation);

2. Subtract A(0) from received samples and extract timing;

3. For n=0, 1, 2 . . . calculate iterative solution${\overset{\rightarrow}{h}\left( {n + 1} \right)} = {{\left( {\frac{1}{M}{\sum\limits_{k = 1}^{M}{{\overset{\rightarrow}{b}(k)}{{\overset{\rightarrow}{b}}^{H}(k)}}}} \right)^{- 1}\frac{1}{M}{\sum\limits_{k = 1}^{M}{{\overset{\rightarrow}{b}(k)}\left\lbrack {{r(k)} - {A(n)}} \right\rbrack}^{*}}} = {\frac{1}{M}{\sum\limits_{k = 1}^{M}{{\overset{\rightarrow}{b}(k)}\left\lbrack {{r(k)} - {A(n)}} \right\rbrack}}}}$${A\left( {n + 1} \right)} = {\frac{1}{M}{\sum\limits_{k = 1}^{M}\left\lbrack {{r(k)} - {\left( {\overset{\rightarrow}{h}\left( {n + 1} \right)} \right)^{H}{\overset{\rightarrow}{b}(k)}}} \right\rbrack}}$

The DC offset estimate, A(n+1), can be calculated over the mid-amblelength or entire burst length, N; and

4. Subtract the final DC offset value from received samples for furtherprocessing.

It is important to note that the index n in iterations does notcorrespond to time index as in LMS solution, but rather it correspondsto the iteration step. Matrix inversion is avoided due tocross-correlation properties of the mid-amble in the GSM system, so thatthe channel estimate is a simple cross-correlation with known bitsequence. The number of iterations required has to be determined viasimulation.

Thus, referring to FIG. 6, the DSP 52 is programmed by a memory storedin the DSP 52 in accordance with the flowchart shown in FIG. 6, toperform the following method on the received signal, r(k):

In step 300, the received burst samples, r(k), are stored in a memoryprovided in the DSP 52. In the next step, 302, an initial DC offset,A(0), is calculated from the received samples as the average value overthe burst. In the next step 304, the initial DC offset, A(0), issubtracted from the received burst. In the next step 306, the channelimpulse response (coefficient vector value)${\overset{\rightarrow}{h}\left( {n + 1} \right)} = {\frac{1}{M}{\sum\limits_{k = 1}^{M}{{\overset{\rightarrow}{b}(k)}\left\lbrack {{r(k)} - {A(n)}} \right\rbrack}^{*}}}$

are updated. In the next step 308, the DC offset value, (calculated overthe mid-amble length with known bits or the over the whole burst withdecoded bits, i.e., a tentative decision of the information bits)${A\left( {n + 1} \right)} = {\frac{1}{M}{\sum\limits_{k = 1}^{M}\quad \left\lbrack {{r(k)} - {\left( {\overset{->}{h}\left( {n + 1} \right)} \right)^{H}{\overset{->}{b}(k)}}} \right\rbrack}}$

are updated. In the next step 310, a determination is made as to whetherthe number of required iterations, P, been performed (i.e., have thenumber of required iterations, P, been performed? If not, the processcontinues to update the estimated channel impulse response (i.e.,coefficients) and DC offset values, the process returns to step 306; ifit has, the computed DC offset A(P) and channel impulse response(coefficient) vector {right arrow over (h)}(P) is forwarded to thechannel receiver, step 312.

Simulation Results

To quantify the performance improvement obtained by performing jointestimation of DC offset and channel impulse response (i.e.,coefficients), simulations have been carried out. The first set ofsimulations in Matlab compares the probability density functions of theDC offset estimation error for sample mean estimator and jointestimator. The estimation error has been analyzed over a 1000 burstusing a quasi-static channel modeling (fixed fading channel coefficientsduring the burst) and applying serial receiver analysis where DC offsethas been added to the In-phase component of the signal after the signalde-rotation. Two scenarios have been analyzed: a high SNR (no noise)case and a low SNR=8 dB, and the results have been presented in FIGS. 7,8, and 9 and TABLES I and II, below.

TABLE I, Statistical Parameters of DC Offset Estimation Error for SampleMean—Averaging Estimator (AE) and Joint Estimator (JE) Performed Overthe Whole Burst N (JE-N) for High SNR (No Noise)

Static TU HT RA Mean-AE 0.12 0.001 0.002 0.0016 Std-AE 0.075 0.1 0.1 0.1Mean-JE-N 0.004 1e-4 2e-4 6e-5 Std-JE-N 0.045 0.045 0.05 0.045

where Static refers to a direct connection in place of antennas for theradio propagation channel 26 (FIG. 2); RA is Rural Area; TU is TypicalUrban Area; and, HT is Hilly Terrain, as defined by the ETSI. Further,“Mean” refers to statistical mean and Std refers to standard deviation.In high SNR case joint estimation eliminates the bias component of theDC offset residual in static channel, which is direct consequence of themodulated signal presence. At the same time in all channel conditions itreduced the variance of the estimate. The reduction in standardvariation is about two times as quantified in Table I.

In low SNR case standard deviation of both estimators is higher due toadditional thermal noise. Joint estimator performed over the burstlength eliminates bias for he static channel and reduces standarddeviation by a factor of two as quantified in Table II. When jointestimation is performed over midamble length to reduce the computationalcomplexity a few observations can be made. In all channel conditionsstandard deviation of the estimate has been larger since the sample sizeis smaller (midamble length versus whole burst). In static channelresidual DC offset is eliminated, while variance is comparable to thesample mean case. In fading channels residual DC offset is two timessmaller and standard deviation is 10% smaller when using jointestimation.

TABLE II, Statistical Parameters of DC Offset Estimation Error forSample Mean—Averaging Estimator (AE) and Joint Estimator (JE) PerformedOver the Whole Burst N(JE-N) and the Joint Estimator Performed Over theMid-amble Length M(JE-M). for SNR=8 dB

Static TU HT PA Mean-AE 0.12 0.004 0.003 0.004 Std-AE 0.08 0.11 0.110.11 Mean-JE-N 0.005 4e-4 4e-4 9e-5 Std-JE-N .055 .054 .056 .055Mean-JE-M .0001 .002 .001 .001 Std-JE-M 0.097 0.1 0.1 0.1

To quantify the impact on BER, Matlab simulations have been carried outfor the static channel and summarized in FIG. 10.

A few assumptions have been made, as follows:

1. The DC offset had random value up to 50 dB above the modulated signalwith uniform distribution;

2. The DC offset was constant during the burst duration; and

3. The joint estimation technique has assumed the least compleximplementation (i.e. single iteration for least-squares solution):

(a) An initial DC estimate by averaging over the burst

(b) A calculation of a 5-tap Channel Impulse Response (CIR) afterinitial DC subtraction

(c) A modification of the DC estimate by subtracting the modulatedsignal is obtained by passing data bits from the entire burst (no errorsin decision) through estimated CIR and averaging over the burstafterwards; and

(d) A final Channel Impulse Response (CIR) estimation for the datareceiver 34 is made after subtracting the DC estimate from the receivedsignal.

As shown in FIG. 10, the joint DC offset compensation performed over theentire burst mength N (JE-N) has the potential of completely eliminatingthe performance degradation due to residual DC offset introduced bysample mean estimator. Performing the joint estimation over midamblelength (JE-M) results in a loss of the order of 0.1 dB for SNR less than8 dB, and no less for SNR larger than 8 dB.

Other embodiments are within the spirit and scope of the appendedclaims. For example, while the invention has been described above forreducing DC offsets in a direct conversion receiver, the invention maybe used with other types of receivers, such as heterodyne receivers.Further, the invention may be used with systems other then GSM.

What is claimed is:
 1. A method of compensating for DC offset in areceiver, said method comprising: receiving a signal burst from atransmitter device; storing said signal burst in a memory device;performing joint and simultaneous Minimum Mean Square Error optimizationwith respect to a DC offset and a channel impulse associated with saidsignal burst so that a computed DC offset and a computed channel impulseare generated; subtracting from said signal burst said computed DCoffset forming a second signal burst indicative of said DC offset beingremoved from said signal burst; and using said computed channel impulseto equalize said second signal burst so as to compute modulatedcomponents of said received signal burst.
 2. The method of claim 1,wherein said signal burst is defined asr(k) = A + ∑b(n)h(k − n) + N(k)

where A is said DC offset, b(n) are data symbols, h(k) is said channelimpulse, k is a time index, and N(k) is thermal noise.
 3. The method ofclaim 2, wherein said Minimum Mean Square Error optimization is definedas$\frac{\partial\left( {f\left( {e(k)} \right)} \right)}{{\partial\hat{A}}\quad} = {{0\quad {and}\quad \frac{\partial\left( {f\left( {e(k)} \right)} \right)}{\partial\hat{h}}} = 0}$

where e(k) is an error function, f(e(k)) is a Minimum Mean Square Errorfunction, Â is the computed DC offset, and ĥ is the computed channelimpulse.
 4. The method of claim 2, wherein said computed DC offset is astatistical average of r(k)−{right arrow over (h)} ₀ ^(H) {right arrowover (b)}(k) where r(k) is said signal burst, {right arrow over (h)}₀ issaid computed channel impulse, and b(k) is said data symbols.
 5. Themethod of claim 2, wherein said computed channel impulse is defined asE{{right arrow over (b)}(k){right arrow over (b)} ^(H)(k)}⁻¹ E{{rightarrow over (b)}(k)[r(k)−A ₀]*} where E{} is a statistical averageoperator, {right arrow over (b)}(k) is a vector associated with saiddata symbols, r(k) is said signal burst, and A₀ is said computed DCoffset.
 6. An apparatus for reducing DC offset in a receiver comprising:a data receiver that receives a signal burst from a transmitter device,said data receiver storing said signal burst in a memory device; and aDSP device that performs joint and simultaneous Minimum Mean SquareError optimization with respect to a DC offset and a channel impulseassociated with said signal burst so that a computed DC offset and acomputed channel impulse are generated, wherein said DSP devicesubtracting from said signal burst said computed DC offset forming asecond signal burst indicative of said DC offset being removed from saidsignal burst and using said computed channel impulse to equalize saidsecond signal burst so as to compute modulated components of saidreceived signal burst.
 7. The apparatus of claim 6, wherein said signalburst is defined as r(k) = A + ∑b(n)h(k − n) + N(k)

where A is said DC offset, b(n) are data symbols, h(k) is said channelimpulse, k is a time index, and N(k) is thermal noise.
 8. The apparatusof claim 2, wherein said Minimum Mean Square Error optimization isdefined as$\frac{\partial\left( {f\left( {e(k)} \right)} \right)}{{\partial\hat{A}}\quad} = {{0\quad {and}\quad \frac{\partial\left( {f\left( {e(k)} \right)} \right)}{\partial\hat{h}}} = 0}$

where e(k) is an error function, f(e(k)) is a Minimum Mean Square Errorfunction, Â is the computed DC offset, and ĥ is the computed channelimpulse.
 9. The apparatus of claim 7, wherein said computed DC offset isa statistical average of r(k)−{right arrow over (h)} ₀ ^(H) {right arrowover (b)}(k) where r(k) is said signal burst, {right arrow over (h)}₀ issaid computed channel impulse, and b(k) is said data symbols.
 10. Theapparatus of claim 7, wherein said computed channel impulse is definedas E{{right arrow over (b)}(k){right arrow over (b)} ^(H)(k)}⁻¹ E{{rightarrow over (b)}(k)[r(k)−A ₀]*} where E{} is a statistical averageoperator, {right arrow over (b)}(k) is a vector associated with saiddata symbols, r(k) is said signal burst, and A₀ is said computed DCoffset.